Spawning and Reproductive Success of Hatchery Breeders
Comparison of reproductive success in red drum hatchery adults
SJ O’Leary
2022-06-15
Effective number of breeders
Unequal sex ratios and variance in family sizes among mating combinations (sire X dam) can contribute to the effective number of breeders \(N_{b}\) being reduced compared to the potential number of breeders \(N\) contributing to a given spawning event (i.e. brood fish present in spawning tanks).
The maximum effective number of breeders if all pairs (male x female combinations) contribute equally can be calculated as
with \(N_{f}\) and \(N_{m}\) denoting the number of females and males potentially contributing to the spawning event, respectively (???).
Generally, some individuals in a spawning tank will not contribute at all; to determine the reduction in \(N_{b}\) due to some individuals not contributing at all the above equation can be used using the number of male and female broodstock that had progeny assigned to them for \(N_{f}\) and \(N_{m}\).
The effect of variance in family size in reducing the effective number of breeders can be calculated as:
With the effective number of females (\(N_{bf}\)) calculated as
(Equation. 3.1)
\[N_{bf}=\frac{1}{\sum_{k=1}^{n_{f}}q_{k}^2}\]
and the effective number of males (\(N_{bf}\)) calculated as
(Equation. 3.2)
\[N_{bf}=\frac{1}{\sum_{k=1}^{n_{f}}q_{k}^2}\]
with \(N_{f}\) and \(N_{m}\) as the actual number of females and and males contributing to a spawning event, and \(q\) as the proportion of progeny contributed by an adult (Lacy 1989Lacy, Robert C. 1989. “Analysis of founder representation in pedigrees: Founder equivalents and founder genome equivalents.” Zoo Biology 8 (2): 111–23. https://doi.org/10.1002/zoo.1430080203.).
Calculate values of maximum attainable \(N_{b}\) given the number of individuals in tanks contributing to a spawning event, and given the actual number of individuals that did have progeny assigned to them. Determine the effective number of breeders based on variance in family size and calculate the reduction in \(N_{b}\) at each sampling point compared to \(N_{b(max)}\) and the reduction due to the fact that some brood fish do not contribute at all.
Table 1: Comparison of actual and effective number of breeders per spawning event and sample point. Nm and Nf denote the actual number of males and females with progeny assigned to them for a given spawning event/sampling point, N_contrib is the total number of contributing broodfish, Nb(max) is the maximum effective number of breeders if all fish in tanks are successful and contribute equally (Equation 1), Nb(max)’ is the maximum number of effective breeders given the number of males/females that actually had progeny assigned to them, while Nb is the effective number of breeders accounting for variance in family size. Reduct_unsuccessf indicates the reductions in effective number of breeders compared to Nb(max) due to just the fact that some individuals are not successful, while Reduct_variance is the combined effect of both individuals not being successful at all and variance among family size.
E
P
Nm
Nbm
Nf
Nbf
N_tanks
F_tanks
M_tanks
Nb(max)
N_contrib
Nb(max)’
Nb
Reduct_unsuccessf
Reduct_variance
YOY-1
T1
5
3.65
3
2.25
10
5
5
10.0
8
7.50
5.56
0.25
0.44
YOY-1
T2
5
4.01
3
2.28
10
5
5
10.0
8
7.50
5.81
0.25
0.42
YOY-1
T3
5
3.71
3
2.49
10
5
5
10.0
8
7.50
5.95
0.25
0.40
YOY-2
T1
7
5.05
5
3.91
20
11
9
19.8
12
11.67
8.82
0.41
0.55
YOY-2
T2
5
3.36
4
3.11
20
11
9
19.8
9
8.89
6.46
0.55
0.67
YOY-2
T3
7
4.27
5
3.41
20
11
9
19.8
12
11.67
7.59
0.41
0.62
YOY-3
T1
4
1.42
4
1.42
15
9
6
14.4
8
8.00
2.84
0.44
0.80
YOY-3
T2
5
2.58
4
2.55
15
9
6
14.4
9
8.89
5.13
0.38
0.64
YOY-3
T3
5
2.65
4
2.63
15
9
6
14.4
9
8.89
5.28
0.38
0.63
Expected contribution per breeder for each spawning event
Spawning event one, two, and three contained progeny from two, four, and three tanks, respectively. Putatively, each tank contains three females and two males, parentage assignment revealed that one adult assumed to be a female is actually male.
For each spawning event, the expected proportion of progeny assigned per breeder was calculated as the proportion of progeny that should be assigned to a breeder if all breeders of the same sex were to contribute to a spawning event with equal success.
Table 2: Number of males and females per spawning event and expected percent of progeny assigned per breeder if all breeders contribute equally.
SPAWNING_EVENT
SEX
n
PERC_OFFSP
YOY-1
F
5
20.00
YOY-1
M
5
20.00
YOY-2
F
11
9.09
YOY-2
M
9
11.11
YOY-3
F
9
11.11
YOY-3
M
6
16.67
Spawning & reproductive success spawning event 1
Spawning success of an adult was calculated as the proportion of progeny assigned to a given breeder at the first sampling point (T1) and reproductive success as the proportion of progeny assigned to a given breeder at the final sampling point (T3) when fingerlings were removed to be stocked in the bay.
Table 3a: Proportion of progeny assigned per sire for each time point in pond 1
sire
T1
T2
T3
ADULT_3160
0.400
0.277
0.258
ADULT_4098
0.218
0.169
0.274
ADULT_4099
0.136
0.193
0.073
ADULT_4154
0.027
0.036
0.048
ADULT_5341
0.218
0.325
0.347
Table 3b: Proportion of progeny assigned per dam for each time point in pond 1
dam
T1
T2
T3
ADULT_4114
0.091
0.072
0.129
ADULT_5123
0.564
0.506
0.379
ADULT_9436
0.345
0.422
0.492
Table 3c: Proportion of progeny assigned per pair at stocking.
dam
sire
n
frq
ADULT_4114
ADULT_4098
12
0.10
ADULT_4114
ADULT_5341
4
0.03
ADULT_5123
ADULT_3160
32
0.26
ADULT_5123
ADULT_4099
9
0.07
ADULT_5123
ADULT_4154
6
0.05
ADULT_9436
ADULT_4098
22
0.18
ADULT_9436
ADULT_5341
39
0.31
Adults from two spawning tanks contributed to pond 1.
Table 4: Proprtion of expected progeny assigned per breeder if all breeders are equally successful.
SEX
n
PERC_OFFSP
F
5
20
M
5
20
Compare the difference in observed vs. expected number of progeny assigned to each breeder.
Figure 1: Difference of expected and observed proportion of progeny per male and female and total proportion per parent sent per sampling point (breeders that did not have any progeny assigned are not included in figure).
Compare proportion of progeny assigned to pairs of breeders.
Figure 2: Proportion of progeny assigned to pairs of breeders at each sampling point.
Spawning/reproductive success spawning event 2
Spawning success of an adult was calculated as the proportion of progeny assigned to a given adult at the first sampling point (T1) and reproductive success as the proportion of progeny assigned to a given breeder at the final sampling point (T3) when fingerlings were removed to be stocked in the bay.
Table 5a: Proportion of progeny assigned per sire for each time point in pond 2.
sire
T1
T2
T3
ADULT_3160
0.212
0.077
0.102
ADULT_4098
0.017
NA
0.042
ADULT_4134
0.212
0.385
0.390
ADULT_4136
0.110
0.026
0.144
ADULT_4154
0.161
0.333
0.102
ADULT_5081
0.263
0.179
0.195
ADULT_7514
0.025
NA
0.025
Table 5b: Proportion of progeny assigned per dam for each time point in pond 2.
dam
T1
T2
T3
ADULT_5123
0.042
NA
0.068
ADULT_6080
0.203
0.359
0.119
ADULT_7930
0.373
0.205
0.339
ADULT_8155
0.169
0.051
0.085
ADULT_9436
0.212
0.385
0.390
Table 5c: Proportion of progeny assigned per pair at stocking.
dam
sire
n
frq
ADULT_5123
ADULT_4098
5
0.04
ADULT_5123
ADULT_7514
3
0.03
ADULT_6080
ADULT_3160
3
0.03
ADULT_6080
ADULT_4154
11
0.09
ADULT_7930
ADULT_4136
17
0.14
ADULT_7930
ADULT_5081
23
0.19
ADULT_8155
ADULT_3160
9
0.08
ADULT_8155
ADULT_4154
1
0.01
ADULT_9436
ADULT_4134
46
0.39
Adults from four spawning tanks contributed to spawning event 2.
Table 6: Proprtion of expected progeny per breeder if all breeders are equally successful.
SEX
n
PERC_OFFSP
F
11
9.09
M
9
11.11
Compare the difference in observed vs. expected number of progeny assigned to each breeder.
Figure 3: Difference of expected and observed proportion of progeny per male and female and total proportion per parent sent per sampling point (breeders that did not have any progeny assigned are not included in figure).
Compare proportion of progeny assigned to pairs of breeders.
Figure 4: Proportion of progeny assigned to pairs of breeders at each sampling point.
Spawning/reproductive success spawning event 3
Spawning success of an adult was calculated as the proportion of progeny assigned to a given adult at the first sampling point (T1) and reproductive success as the proportion of progeny assigned to a given breeder at the final sampling point (T3) when fingerlings were removed to be stocked in the bay.
Table 7a: Proportion of progeny assigned per sire for each time point in pond 3.
sire
T1
T2
T3
ADULT_3160
NA
0.010
NA
ADULT_4134
0.056
0.152
0.282
ADULT_4136
0.833
0.571
0.526
ADULT_4154
0.037
0.095
0.038
ADULT_5081
NA
NA
0.013
ADULT_8311
0.074
0.171
0.141
Table 7b: Proportion of progeny assigned per dam for each time point in pond 3.
dam
T1
T2
T3
ADULT_4147
0.056
0.200
0.218
ADULT_6080
0.037
0.105
0.038
ADULT_7930
0.833
0.571
0.538
ADULT_9436
0.074
0.124
0.205
Table 7c: Proportion of progeny per pair at stocking.
dam
sire
n
frq
ADULT_4147
ADULT_4134
13
0.17
ADULT_4147
ADULT_8311
4
0.05
ADULT_6080
ADULT_4154
3
0.04
ADULT_7930
ADULT_4136
41
0.53
ADULT_7930
ADULT_5081
1
0.01
ADULT_9436
ADULT_4134
9
0.12
ADULT_9436
ADULT_8311
7
0.09
Adults from three spawning tanks contributed to spawning event 3.
Table 8: Proprtion of expected progeny per breeder if all breeders are equally successful.
SEX
n
PERC_OFFSP
F
9
11.11
M
6
16.67
Compare the difference in observed vs. expected number of progeny assigned to each breeder.
Figure 5: Difference of expected and observed proportion of progeny per male and female and total proportion per set of parents per sampling point (breeders that did not have any progeny assigned are not included in figure).
Compare proportion of progeny assigned to pairs of breeders.
Figure 6: Proportion of progeny assigned to pairs of breeders at each sampling point.
Comparison across spawning events
Comparison expected v realized reproductive success across spawning events
Figure 7: Comparison of expected and realized reproductive success per spawning event and sampling point for male and female broodfish
Compare differences by breeder.
Figure 8: Comparison of expected and realized reproductive success per spawning event and sampling point for male and female broodfish that successfully participated in more than one spawning event.
Family-wise comparisons
Figure 9: Comparison of proportion of progeny assigned to each family (female x male cross) per spawning event and sampling point.
Table 9a: Mean family size (as proportion of total progeny) per spawning event.
SPAWNING_EVENT
mean
sd
min
max
YOY-1
0.143
0.113
0.024
0.400
YOY-2
0.125
0.119
0.008
0.390
YOY-3
0.150
0.223
0.010
0.833
Table 9b: Number of females a male breeds with (putatively three females and two males present in a spawning tank).
SPAWNING_EVENT
mean female partners
YOY-1
1.4
YOY-2
1.3
YOY-3
1.4
Table 9c: Number of males a female breeds with (putatively three females and two males present in a spawning tank).
SPAWNING_EVENT
mean male partners
YOY-1
2.3
YOY-2
1.8
YOY-3
1.8
Comparison of reproductive success among breeders
The proportion of progeny assigned to breeders at sampling points T1 and T3 was compared to identify differences in spawning and reproductive success among and within breeders.
Figure 10: Comparison of proportion of progeny released per pond assigned to each breeder. Breeders that were in the spawning tanks contributing to a spawning event (SPAWNERS = SP) are denoted as filled circles (YOY1 = yellow, YOY2 = turquoise, YOY3 = purple), even if they did not successfully produce progeny. Breeders that were not in the spawning tanks (SPAWNERS = NOT) for a given spawning event are denoted with an x.
Compare across sampling points
Figure 11: Comparison of proportion of progeny assigned to each broodfish per spawning event and sampling point (T1, blue; T2, green, T3, red). Broodstock that were in the spawning tanks contributing to a spawning event (SPAWNERS = SP) are included, even if they did not successfully produce progeny. Breeders that were not in the spawning tanks (SPAWNERS = NOT) for a given spawning event are denoted with an x.
Relationship of age and time spent in hatchery with reproductive success
Estimate approximate age of breeders
Total length and weight was determined for adult red drum caught in the wild and introduced to the hatchery as breeders. Condition at introduction was calculated as the weigt/length ratio (measurements in milimeters and grams). The approximate age at introduction to the hatchery was determined using an age-length regression (Porch, Wilson, and Nieland 2002Porch, Clay E., Charles A. Wilson, and David L. Nieland. 2002. “A new growth model for red drum (sciaenops ocellatus) that accommodates seasonal and ontogenic changes in growth rates.” http://aquaticcommons.org/15199/.) which implements a dampend growth model able to account for a decrease in the growth rate over the lifetime of red drum. Approximate age at spawning was determined as the sum of age at introduction and the time spent in the hatchery.
Determine mean spawning/reproductive success per breeder
Mean reproductive success at sample points T1 and T3 per breeder was determined as the mean proportion of progeny assigned to an adult across spawning events (adults participated in one to three events).
Figure 13: Spawning and reproductive success per breeder/spawning event.
Table 10: Mean spawning and reproductive success per breeder
SAMPLE_ID
SEX
AGE_INTROD
TIME_HATCHERY
MEAN_REPROD
STD_REPROD
MEAN_SPAWN
STD_SPAWN
N_EVENTS
ADULT_4114
F
4.8
0
0.043
0.074
0.030
0.053
3
ADULT_4147
F
3.9
4
0.073
0.126
0.019
0.032
3
ADULT_4148
F
9.6
3
0.000
0.000
0.000
0.000
2
ADULT_4162
F
31.7
4
0.000
0.000
0.000
0.000
2
ADULT_5123
F
9.6
4
0.224
0.220
0.303
0.369
2
ADULT_6080
F
15.0
0
0.078
0.057
0.120
0.117
2
ADULT_7452
F
22.9
6
0.000
0.000
0.000
0.000
2
ADULT_777
F
12.0
6
0.000
0.000
0.000
0.000
2
ADULT_7930
F
15.0
6
0.438
0.141
0.603
0.325
2
ADULT_8155
F
15.0
4
0.042
0.060
0.084
0.120
2
ADULT_9436
F
20.6
5
0.362
0.145
0.210
0.136
3
ADULT_3160
M
16.8
4
0.120
0.130
0.204
0.200
3
ADULT_4098
M
8.6
3
0.158
0.164
0.118
0.142
2
ADULT_4099
M
12.0
2
0.036
0.052
0.068
0.096
2
ADULT_4134
M
3.2
5
0.336
0.076
0.134
0.110
2
ADULT_4136
M
7.7
5
0.335
0.270
0.472
0.511
2
ADULT_4154
M
3.9
4
0.063
0.034
0.075
0.075
3
ADULT_5081
M
9.6
0
0.104
0.129
0.132
0.186
2
ADULT_5341
M
12.0
5
0.347
0.000
0.218
0.000
1
ADULT_7514
M
18.5
0
0.025
0.000
0.025
0.000
1
ADULT_8311
M
3.2
0
0.070
0.100
0.037
0.052
2
Comparison of age related data to reproductive success categories
Breeders that participated in multiple events were categorized as ‘always successful’, ‘not always successful’, and ‘never successful’ and their mean age at introduction, condition, spawning age, and time spent in the hatchery compared.
Table 11: Mean +/- sd of conditioning parameters of broodfish that participated in multiple spawning events.
CATEGORY
n
mean_SPAWN
sd_spawn
mean_INTROD
sd_introd
mean_HATCHERY
sd_hatch
mean_COND
sd_COND
mean_DIFF
sd_DIFF
always
17
13.55294
6.214712
10.55294
5.646693
3.00
2.179450
9.208114
3.213955
-0.0001176
0.0971770
never
4
23.80000
10.435516
19.05000
10.228229
4.75
1.500000
10.953699
1.818621
0.0000000
0.0000000
sometimes
11
15.86364
10.008724
12.86364
8.585717
3.00
2.236068
9.898523
2.966842
0.0078182
0.0375894
The mean age at spawning for breeders that were never successful spawners for any event they participated in is 23.8, they spent a mean 4.75 years in the hatchery and were on average 19.1 years old when introduced to the hatchery.
Similarly, for breeders that were not successful spawners at least once the mean age at spawning is 15.9, they spent 3 years in the hatchery and were 12.9 years old on average when introduced to the hatchery.
In contrast, breeders that were always successful spawners spawn at a mean age of 13.6, spent a mean 3 years in the hatchery, and were introduced to the hatchery at 10.6 years old.
Distribution is not normal and sample sizes differ among the three categories. Test for significant differences among the categories for each condition parameter using Kruskal-Wallis followed by ad post hoc Dunn test to identify pairwise differences. Kruskal Wallis is a non-parametric equivalent of an ANOVA1 ANOVA assumed normal distribution and compares the mean values among two or more groups. and compares the mean ranks (medians) of groups which are less sensitive to outliers than means. It does not assume any specific distribution to calculate test statistics and p-values. Dunn’s test retains the rank sums of the Kruskal-Wallis test to test for pairwise comparisons. Correct for multiple comparisons using Benjamini-Hochberg FDR method (5% cut-off).
Age at spawning
##
## RESULTS KRUSKAL WALLIS
##
## Kruskal-Wallis rank sum test
##
## data: AGE_SPAWN by CATEGORY
## Kruskal-Wallis chi-squared = 2.706, df = 2, p-value = 0.2585
##
##
## RESULTS PAIRWISE COMPARISONS USING DUNN's TEST
## Comparison Z P.unadj P.adj
## 1 always - never -1.6439002 0.1001968 0.3005904
## 2 always - sometimes -0.3923723 0.6947831 0.6947831
## 3 never - sometimes 1.3045906 0.1920323 0.2880484
Age at introduction to hatchery
##
## RESULTS KRUSKAL WALLIS
##
## Kruskal-Wallis rank sum test
##
## data: AGE_INTROD by CATEGORY
## Kruskal-Wallis chi-squared = 2.5678, df = 2, p-value = 0.277
##
##
## RESULTS PAIRWISE COMPARISONS USING DUNN's TEST
## Comparison Z P.unadj P.adj
## 1 always - never -1.5944562 0.1108339 0.3325017
## 2 always - sometimes -0.5896898 0.5553986 0.5553986
## 3 never - sometimes 1.1267619 0.2598431 0.3897647
Time spent in hatchery
##
## RESULTS KRUSKAL WALLIS
##
## Kruskal-Wallis rank sum test
##
## data: TIME_HATCHERY by CATEGORY
## Kruskal-Wallis chi-squared = 2.0707, df = 2, p-value = 0.3551
##
##
## RESULTS PAIRWISE COMPARISONS USING DUNN's TEST
## Comparison Z P.unadj P.adj
## 1 always - never -1.3458238 0.1783594 0.2675390
## 2 always - sometimes 0.1218043 0.9030540 0.9030540
## 3 never - sometimes 1.3616500 0.1733084 0.5199251
Condition at introduction
##
## RESULTS KRUSKAL WALLIS
##
## Kruskal-Wallis rank sum test
##
## data: COND_INTROD by CATEGORY
## Kruskal-Wallis chi-squared = 1.9075, df = 2, p-value = 0.3853
##
##
## RESULTS PAIRWISE COMPARISONS USING DUNN's TEST
## Comparison Z P.unadj P.adj
## 1 always - never -1.3356776 0.1816547 0.5449640
## 2 always - sometimes -0.7179734 0.4727737 0.4727737
## 3 never - sometimes 0.7971827 0.4253449 0.6380174
Difference reproductive success T1-T3
##
## RESULTS KRUSKAL WALLIS
##
## Kruskal-Wallis rank sum test
##
## data: DIFF_SUCCESS by CATEGORY
## Kruskal-Wallis chi-squared = 0.12295, df = 2, p-value = 0.9404
##
##
## RESULTS PAIRWISE COMPARISONS USING DUNN's TEST
## Comparison Z P.unadj P.adj
## 1 always - never 0.34823203 0.7276659 1.0000000
## 2 always - sometimes 0.05664437 0.9548285 0.9548285
## 3 never - sometimes -0.29389964 0.7688346 1.0000000
Compare median of distribution of observations
Figure 14: Distribution of mean age at spawning, mean at at introduction to the hatchery, and time spent in the hatchery before spawning event for breeders that participated in multiple spawning events. Breeders are grouped as always successful (green), sometimes successful (yellow), and never successful (red).
Comparison of reproductive success at T1 and T3 and conditioning parameters
Spearman Rank correlation coefficient is a rank-based (non-parametric) measure of statistical dependence to assess who well relationship of X and Y can be described using a monotone function i.e. Y either strictly increases (or decreases) as X increases even if that relationship is not linear (Y does not increase by same increment for every increment of X).
Figure 15: Reproductive success at sampling point T1 related to conditioning parameters using each spawning event as an independent observation.
Figure 16: Reproductive success at sampling point T3 related to conditioning parameters using each spawning event as an independent observation.
